Indicate the coordination number for the central metal atom in each of the following coordination compounds: (a) \(\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2} \mathrm{Br}_{2}\right]\) (b) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)(\mathrm{py})(\mathrm{Cl})(\mathrm{Br})\right]\) ( \(\mathrm{py}=\) pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}\) ) (c) \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]\) (d) \(\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)(\mathrm{py})(\mathrm{Cl})(\mathrm{Br})\right]\) (e) \(\left[\mathrm{Ni}_{\mathrm{i}}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4} \mathrm{Cl}_{21}\right]\) (f) \(\left[\mathrm{Fe}(\mathrm{en})_{2}(\mathrm{CN})_{21}^{+}\left(\mathrm{en}=\text { ethylenediamine }, \mathrm{C}_{2} \mathrm{H}_{8} \mathrm{N}_{2}\right)\right.\)

Coordination compounds, comprising of central metal atoms or ions surrounded by molecules or anions called ligands, represent a fascinating area of chemistry that plays a pivotal role in both our understanding of chemical reactivity and the development of new materials. The ligands donate electron pairs to the metal, thereby forming coordinate covalent bonds.

Central to understanding these compounds is the concept of the coordination number, which represents the number of ligand atoms bonded to a central metal ion. For example, in the compound \(\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\mathrm{Br}_{2}\right]\), the platinum ion is surrounded by a total of four atoms from its ligands—two oxygen atoms from water molecules and two bromine ions—giving it a coordination number of four.

This concept is crucial when predicting the geometry and reactivity of metal complexes as well, making it an essential part of any study in inorganic chemistry. Remember, don't be confused by subscripts or complex naming conventions; the coordination number is all about counting the connections directly to the central metal.

In coordination chemistry, ligands are the 'supporting characters' that determine the plot of the compound's structure and reactivity. Ligands can be as simple as water \(\mathrm{H}_{2}\mathrm{O}\) or as complex as the ethylenediamine \(\mathrm{en}\), serving as bridges between the metal and the rest of the chemical world.

Ligands can donate one or multiple electron pairs, classified as monodentate, bidentate, or polydentate. Monodentate ligands like \(\mathrm{NH}_{3}\) or \(\mathrm{Cl}^{-}\) bind through a singular atom, while bidentate ligands like ethylenediamine have two binding sites that allow them to hold the central metal more securely. In the compound \(\left[\mathrm{Fe}(\mathrm{en})_{2}(\mathrm{CN})_{2}\right]^{+}\), the ethylenediamine is a bidentate ligand, wrapping around the iron ion for a more stable complex.

The choice of ligands in the formation of coordination compounds is not accidental; it deeply influences the properties and potential applications, from catalysis to biomedical imaging.

Transition metals are like the versatile actors of the periodic table, capable of playing various roles thanks to their unique ability to adopt multiple oxidation states and coordination environments. This versatility makes them perfect for starring in coordination compounds.

Their d-orbitals allow transition metals to form complex geometries and bonding associations that are not possible for other elements. For example, in \(\left[\mathrm{Ni}_{\mathrm{i}}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\mathrm{Cl}_{2}\right]\), if we correct the notation to \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\mathrm{Cl}_{2}\right]\), nickel adopts an octahedral geometry with a coordination number of six, typical for many transition metal complexes.

The chemistry of transition metals isn't just academically stimulating—it's also incredibly practical, finding applications in areas like catalysis, materials science, and even medicine. Whether they are in the active site of an enzyme or the vibrant compound giving color to a material, transition metals are integral to both human civilization and the natural world.